Antigrav, you need to get in touch with the battery manufacturer you are going to use and get his datasheet for the specific battery you are going to recommend. Most batteries are rated for an 8 hour discharge time (except for Gel Cell who uses a 12 hour rate) at 20 degrees C. If you discharge faster, you don’t get as many AH as specified. If you discharge over a longer, you get more than stated. Also, don’t forget to include a derating factor for aging of the battery before use. In your case, you are discharging faster than the specified rate and I estimate that you will be doing well if you get it to last 3 hours, 27 minutes at 20 C. So until you get the derating curves for the specific battery, I would not promise more than 3 hours. On the other hand, a 12 AH battery will last 8 hours.
By getting into bed with a specific manufacturer, you can ensure that your device will outperform what you state because you can use the worst case numbers from the datasheet and if the customer uses a different brand and is unhappy with the results, you can always say “I told you so” then sell him what you know will work.